The names of the protagonists are derived from the Greek words ‘aster’ (star) and ‘phil’ (lover), and the Latin word ’stella’ meaning star.  Thus Astrophel is the star lover, and Stella is his star.  There are 108 Sonnets in all, and 11 songs.   I’ve included links to the first 60 of them, which is more than enough to give you a sense of the form.  If you’d like to hear them all, they’re available here.

Sidney’s form is (with a few exceptions) a variation on the Petrarchan sonnet: 14 lines, rhyme scheme abababab cdcd ee, with a rhyming couplet at the end. Here’s the text of the first sonnet.

1

Loving in truth, and fain in verse my love to show,
That the dear She might take some pleasure of my pain:
Pleasure might cause her read, reading might make her know,
Knowledge might pity win, and pity grace obtain,
I sought fit words to paint the blackest face of woe,
Studying inventions fine, her wits to entertain:
Oft turning others’ leaves to see if thence would flow
Some fresh and fruitful showers upon my sun-burned brain.
But words came halting forth, wanting Invention’s stay,
Invention, Nature’s child, fled step-dame Study’s blows,
And others’ feet still seemed but strangers in my way.
Thus great with child to speak, and helpless in my throes,
Biting my truant pen, beating myself for spite,
‘Fool’ said my Muse to me, ‘look in thy heart and write.’

Other texts to look out for are A Defense of Poesy and The Countess of Pembroke’s Arcadia.

Further Reading:

Sir Philip Sidney page at Vade Mecum
Luminarium Site – includes full text of selected works.